Question

a geometric sequence is defined using the following rulef(1)=4 and f(n)=f(n-1).2find the fourth term of the sequence.show how you arrived at your answer.

Answer 1

`a_4=-32`

Explanation:

We have that the formula of the geometric sequence has the following form:

`\begin{gathered} a_n=a_1\cdot r^(n-1) \\ \end{gathered}`

We have the following information

`\begin{gathered} f(1)=4 \\ \text{therefore:} \\ a_1=4 \\ f(n)=f(n-1)\cdot-2 \\ \text{therefore:} \\ r=-2 \\ \text{replacing} \\ a_n=4\cdot(-2)^(n-1) \end{gathered}`

In the case that n = 4, we replace

`\begin{gathered} a_4=4\cdot(-2)^(4-1) \\ a_4=4\cdot-8 \\ a_4=-32 \end{gathered}`